Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
string bs(long long int left, long long int right, long long int val) {
  while (left <= right) {
    long long int l = left * (left + 1) / 2, r = right * (right + 1) / 2;
    if (l + r == val) {
      return "YES";
    } else if (l + r > val) {
      right--;
    } else {
      left++;
    }
  }
  return "NO";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int n;
  cin >> n;
  long long int right = ceil((-1.0 + sqrt(1 * 1 * 1.0 + 4 * 1 * 2 * n)) / 2);
  cout << bs(1, right, n) << '\n';
}